
from __future__ import annotations

from typing import Any




class 			UpperCAmelCase_     :


  '''simple docstring'''







  def __init__(					self     :					int     ,				UpperCamelCase__     :					int     ,				UpperCamelCase__     :					int     ,				UpperCamelCase__     :					float = 0       )     ->      None:







    """simple docstring"""






    __magic_name__	,       __magic_name__								=			row, column
    __magic_name__								=			[[default_value for c in range(UpperCamelCase__       )] for r in range(UpperCamelCase__       )]
  def __str__(					self     :					Any       )     ->      str:







    """simple docstring"""






    __magic_name__								=			F'''Matrix consist of {self.row} rows and {self.column} columns\n'''

    # Make string identifier
    __magic_name__								=			0
    for row_vector in self.array:
      for obj in row_vector:
        __magic_name__								=			max(UpperCamelCase__     ,				len(str(UpperCamelCase__       )       )       )
    __magic_name__								=			F'''%{max_element_length}s'''

    # Make string and return
    def single_line(UpperCamelCase__     :					list[float]       ) -> str:
      nonlocal string_format_identifier
      __magic_name__								=			"""["""
      line += ", ".join(string_format_identifier % (obj,) for obj in row_vector       )
      line += "]"
      return line

    s += "\n".join(single_line(UpperCamelCase__       ) for row_vector in self.array       )
    return s
  def __repr__(					self     :					List[str]       )     ->      str:







    """simple docstring"""






    return str(self       )
  def 				_lowercase				(					self     :					str     ,				UpperCamelCase__     :					tuple[int, int]       )     ->      bool:







    """simple docstring"""






    if not (isinstance(UpperCamelCase__     ,				(list, tuple)       ) and len(UpperCamelCase__       ) == 2):
      return False
    elif not (0 <= loc[0] < self.row and 0 <= loc[1] < self.column):
      return False
    else:
      return True
  def __getitem__(					self     :					List[str]     ,				UpperCamelCase__     :					tuple[int, int]       )     ->      Any:







    """simple docstring"""






    assert self.validate_indicies(UpperCamelCase__       )
    return self.array[loc[0]][loc[1]]
  def __setitem__(					self     :					List[Any]     ,				UpperCamelCase__     :					tuple[int, int]     ,				UpperCamelCase__     :					float       )     ->      None:







    """simple docstring"""






    assert self.validate_indicies(UpperCamelCase__       )
    __magic_name__								=			value
  def __add__(					self     :					int     ,				UpperCamelCase__     :					Matrix       )     ->      Matrix:







    """simple docstring"""






    assert isinstance(UpperCamelCase__     ,				UpperCamelCase__       )
    assert self.row == another.row and self.column == another.column

    # Add
    __magic_name__								=			Matrix(self.row     ,				self.column       )
    for r in range(self.row       ):
      for c in range(self.column       ):
        __magic_name__								=			self[r, c] + another[r, c]
    return result
  def __neg__(					self     :					Any       )     ->      Matrix:







    """simple docstring"""






    __magic_name__								=			Matrix(self.row     ,				self.column       )
    for r in range(self.row       ):
      for c in range(self.column       ):
        __magic_name__								=			-self[r, c]
    return result
  def __sub__(					self     :					str     ,				UpperCamelCase__     :					Matrix       )     ->      Matrix:







    """simple docstring"""






    return self + (-another)
  def __mul__(					self     :					Optional[int]     ,				UpperCamelCase__     :					int | float | Matrix       )     ->      Matrix:







    """simple docstring"""






    if isinstance(UpperCamelCase__     ,				(int, float)       ):  # Scalar multiplication
      __magic_name__								=			Matrix(self.row     ,				self.column       )
      for r in range(self.row       ):
        for c in range(self.column       ):
          __magic_name__								=			self[r, c] * another
      return result
    elif isinstance(UpperCamelCase__     ,				UpperCamelCase__       ):  # Matrix multiplication
      assert self.column == another.row
      __magic_name__								=			Matrix(self.row     ,				another.column       )
      for r in range(self.row       ):
        for c in range(another.column       ):
          for i in range(self.column       ):
            result[r, c] += self[r, i] * another[i, c]
      return result
    else:
      __magic_name__								=			F'''Unsupported type given for another ({type(UpperCamelCase__       )})'''
      raise TypeError(UpperCamelCase__       )
  def 				_lowercase				(					self     :					List[str]       )     ->      Matrix:







    """simple docstring"""






    __magic_name__								=			Matrix(self.column     ,				self.row       )
    for r in range(self.row       ):
      for c in range(self.column       ):
        __magic_name__								=			self[r, c]
    return result





  def 				_lowercase				(					self     :					Optional[int]     ,				UpperCamelCase__     :					Matrix     ,				UpperCamelCase__     :					Matrix       )     ->      Any:







    """simple docstring"""






    assert isinstance(UpperCamelCase__     ,				UpperCamelCase__       ) and isinstance(UpperCamelCase__     ,				UpperCamelCase__       )
    assert self.row == self.column == u.row == v.row  # u, v should be column vector
    assert u.column == v.column == 1  # u, v should be column vector

    # Calculate
    __magic_name__								=			v.transpose()
    __magic_name__								=			(v_t * self * u)[0, 0] + 1
    if numerator_factor == 0:
      return None  # It's not invertable
    return self - ((self * u) * (v_t * self) * (1.0 / numerator_factor))


# Testing
if __name__ == "__main__":

    def a__       (			):






      '''simple docstring'''





      __magic_name__								=			Matrix(3,	3,	0   )
      for i in range(3   ):
        __magic_name__								=			1
      print(f'''a^(-1) is {ainv}'''   )
      # u, v
      __magic_name__								=			Matrix(3,	1,	0   )
      __magic_name__	,       __magic_name__	,       __magic_name__								=			1, 2, -3
      __magic_name__								=			Matrix(3,	1,	0   )
      __magic_name__	,       __magic_name__	,       __magic_name__								=			4, -2, 5
      print(f'''u is {u}'''   )
      print(f'''v is {v}'''   )
      print(f'''uv^T is {u * v.transpose()}'''   )
      # Sherman Morrison
      print(f'''(a + uv^T)^(-1) is {ainv.sherman_morrison(A_,	A_   )}'''   )

    def a__       (			):






      '''simple docstring'''





      import doctest

      doctest.testmod()





    testa()



from maths.is_square_free import is_square_free
from maths.prime_factors import prime_factors

def a__       (			A_   ):






  '''simple docstring'''





  __magic_name__								=			prime_factors(A_   )
  if is_square_free(A_   ):
    return -1 if len(A_   ) % 2 else 1
  return 0


if __name__ == "__main__":
    import doctest

    doctest.testmod()

